3 TAC5x1x and TAC5x1x-Q1 Digital Biquad Filters

The TAC5x1x and TAC5x1x-Q1 devices support up to three programmable digital biquad filters in the signal chain of each recording and playback channel, shown in Figure 1-1 and Figure 1-2 respectively. By default, each biquad filter acts as an all-pass filter, with a flat gain of 0dB across frequency. By changing the programmable coefficients of these biquad filters, the frequency response can be changed.

Equation 3 shows the quantized 32-bit transfer function of each biquad filter. The coefficients of the filter [N₀,N₁,N₂,D₁ and D₂] are programmable 32-bit twos-complement values, each occupying four consecutive registers in the register space of the device. With the Q-point located in the 31^st bit location (Q31), the filter coefficients are in 1.31 format with a range from –1 (0x80000000) to 0.9999999995 (0x7FFFFFFF). In this notation, the decimal point is assumed to be between bit 30 and bit 31. Bit 31 contains the sign bit, while bits 30-0 contain the fractional bits as shown in Figure 3-1. With this notation, all coefficients are normalized to less than 1. To convert a floating point number less than one to Q31 format, multiply the floating point number by 2³¹ and truncate to the nearest integer. With this notation, the number 1, corresponding to a₀ in the denominator, becomes 2³¹ (0x7FFFFFF). Note that the coefficients N₁ and D₁ are multiplied by two. Thus, when using a digital filter design package to calculate these coefficients, divide by 2 the N₁ and D₁ before writing these coefficient registers. Also, note that coefficients D₁ and D₂ have a negative sign. So, multiply by –1 before writing D₁ and D₂ to the coefficient registers when using a digital filter design package.